Turbulent acceleration of electrons by large-amplitude magnetohydrodynamic waves in solar flares

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Table 1.

Plasma parameters in the outflow region of typical GOES M- and X-class flares.

Plasma parameter	Values
N_e(cm⁻³)	7.0 × 10¹⁰
B(G)	400
T(MK)	22
k_BT(keV)	1.90
ω_pe(s⁻¹)	1.49 × 10¹⁰
ω_pi(s⁻¹)	3.48 × 10⁸
ω_ce(s⁻¹)	7.03 × 10⁹
v_th, e(km s⁻¹)	18 300
c_s(km s⁻¹)	710
v_A(km s⁻¹)	3060
λ_De(cm)	0.12
d_i(cm)	86
r_L, e(cm)	0.26
$λ_{De}^{3} N_{e}$ $Mathematical equation: $ \lambda_{De}^{3}N_{e} $$	1.21 × 10⁸
$c_{s}^{2} / v_{A}^{2}$ $Mathematical equation: $ c_{s}^{2}/v_{A}^{2} $$	0.05
ω_pe/ω_ce	2.12
d_i/r_L, e	330

Notes. N_e, electron number density; B, magnetic field strength; T, temperature; k_BT, thermal energy (k_B, Boltzmann’s constant); ω_pe = (4πe²N_e/m_e)^1/2, electron plasma frequency (e, elementary charge; m_e, electron mass); ω_pi = (4πe²N_e/m_p)^1/2, proton plasma frequency (m_p, proton mass); ω_ce = eB/m_ec, electron cyclotron frequency (c, velocity of light); v_th, e = (k_BT/m_e)^1/2, thermal electron velocity; $c_{s} = {(γ k_{B} T / \tilde{μ} m_{p})}^{1 / 2}$ $Mathematical equation: $ c_{s} = (\gamma k_{\mathrm{B}}T/\tilde \mu m_{p})^{1/2} $$ , sound speed (γ = 5/3, ratio of specific heats; $\tilde{μ} = 0.6$ $Mathematical equation: $ \tilde \mu = 0.6 $$ , mean molecular weight; Priest 1982); $v_{A} = B / {(4 π \tilde{μ} m_{p} 1, 93 N_{e})}^{1 / 2}$ $Mathematical equation: $ v_{A} = B/(4\pi \tilde \mu m_{p} 1,93N_{e})^{1/2} $$ , Alfvén speed (Mann et al. 2024); λ_De = v_th, e/ω_pe, Debye length; d_i = c/ω_pi, ion inertial length; r_L, e = v_th, e/ω_ce, electron gyroradius.

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